Question

please do by java
P14.6 Implement the radix sort algorithm described in Exercise R14.22 (below) to sort arrays of numbers between 0 and 999. P14.7 Implement the radix sort algorithm described in Exercise R14.22 (below) to sort arrays of numbers between 0 and 999. However, use a single auxiliary array, not ten. .P14.8 Implement the radix sort algorithm described in Exercise R14.22 (below) to sort arbitrary int values (positive or negative

Answer 1

The Radix Sort Algorithm 1) Do following for each digit i where i varies from least significant digit to the most significant digit .._........... . a) Sort input array using counting sort (or any stable sort) according to the i'th digit Example: Original, unsorted list: 170, 45, 75, 90, 802, 24, 2, 66 Sorting by least significant digit (1s place) gives: ['Notice that we keep 802 before 2, because 802 occurred before 2 in the original list, and similarly for pairs 170 & 90 and 45 & 75.] 170, 90, 802, 2, 24, 45, 75, 66 Sorting by next digit (10s place) gives: ['Notice that 802 again comes before 2 as 802 comes before 2 in the previous list.] 802, 2, 24, 45, 66, 170, 75, 90 Sorting by most significant digit (100s place) gives: 2, 24, 45, 66, 75, 90, 170, 802

What is the running time of Radix Sort? Let there be d digits in input integers. Radix Sort takes O(d (n+b)) time where b is the base for representing numbers, for example, for decimal system, b is 10. What is the value of d? If k is the maximum possible value, then d would be O(logb(k)). So overall time complexity is O(n+b) * logb(k)). Which looks more than the time complexity of comparison based sorting algorithms for a large k. Let us first limit k. Let k <= nc where c is a constant. In that case, the complexity becomes O(nLogb(n)). But it still doesn't beat comparison based sorting algorithms. What if we make value of b larger?. What should be the value of b to make the time complexity linear? If we set b as n, we get the time complexity as O(n). In other words, we can sort an ar- ray of integers with range from 1 to nc if the numbers are represented in base n (or every digit takes log2(n) bits).

import java.util.*;

public class RadixSort {

    // A utility function to get maximum value in arr[]
    static int getMax(int arr[], int n)
    {
        int mx = arr[0];
        for (int i = 1; i < n; i++)
            if (arr[i] > mx)
                mx = arr[i];
        return mx;
    }

    // A function to do counting sort of arr[] according to
    // the digit represented by exp.
    static void countSort(int arr[], int n, int exp)
    {
        int output[] = new int[n]; // output array
        int i;
        int count[] = new int[10];
        Arrays.fill(count,0);

        // Store count of occurrences in count[]
        for (i = 0; i < n; i++)
            count[ (arr[i]/exp)%10 ]++;

        // Change count[i] so that count[i] now contains
        // actual position of this digit in output[]
        for (i = 1; i < 10; i++)
            count[i] += count[i - 1];

        // Build the output array
        for (i = n - 1; i >= 0; i--)
        {
            output[count[ (arr[i]/exp)%10 ] - 1] = arr[i];
            count[ (arr[i]/exp)%10 ]--;
        }

        // Copy the output array to arr[], so that arr[] now
        // contains sorted numbers according to curent digit
        for (i = 0; i < n; i++)
            arr[i] = output[i];
    }

    // The main function to that sorts arr[] of size n using
    // Radix Sort
    static void radixsort(int arr[], int n)
    {
        // Find the maximum number to know number of digits
        int m = getMax(arr, n);

        // Do counting sort for every digit. Note that instead
        // of passing digit number, exp is passed. exp is 10^i
        // where i is current digit number
        for (int exp = 1; m/exp > 0; exp *= 10)
            countSort(arr, n, exp);
    }

    // A utility function to print an array
    static void print(int arr[], int n)
    {
        for (int i=0; i<n; i++)
            System.out.print(arr[i]+" ");
    }


    /*Driver function to check for above function*/
    public static void main (String[] args)
    {
        int arr[] = {170, 45, 75, 90, 802, 24, 2, 66};
        int n = arr.length;
        radixsort(arr, n);
        print(arr, n);
    }
}

Output:

2 24 45 66 75 90 170 802
Process finished with exit code 0